Lucky numbers of Euler

Lucky numbers of Euler

Euler's "lucky" numbers are positive integers "n" such that "m"2 − "m" + "n" is a prime number for "m" = 0, …, "n" − 1.

Leonhard Euler published the polynomial "x"2 − "x" + 41 which produces prime numbers for all values of "x" from 0 to 40. Obviously, when "x" is equal to 41, the value cannot be prime any more since it is divisible by 41. Only 6 numbers have this property, namely 2, 3, 5, 11, 17 and 41 OEIS|id=A014556.

These numbers are not related to the so-called lucky numbers.

ee also

*Heegner number
* List of topics named after Leonhard Euler
* Formula for primes

References

* F. Le Lionnais, Les Nombres Remarquables. Paris: Hermann, pp. 88 and 144, 1983.

External links

*


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